Learning Objective 1 Explain the two assumptions frequently used in cost-behavior estimation. Determining How Costs Behave – Chapter10

Assumptions in Cost-Behavior Estimation Changes in total costs can be explained by changes in the level of a single activity. Cost behavior can adequately be approximated by a linear function of the activity level within the relevant range.

Learning Objective 2 Describe linear cost functions and three common ways in which they behave.

Cost Function What is a cost function? It is a mathematical expression describing how costs change with changes in the level of an activity.

Cost Function La Playa Hotel offers an airline three alternative cost structures to accommodate its crew overnight: 1. $60 per night per room usage y = $60x The slope of the cost function is $60.

Cost Function

Cost Function 2. $8,000 per month y = $8,000 $8,000 is called a constant or intercept. The slope of the cost function is zero.

Cost Function

Cost Function 3. $3,000 per month plus $24 per room This is an example of a mixed cost. y = $3,000 + $24x y = a + bx

Cost Function

Cost Classification and Estimation Function Choice of cost object Time span Relevant range

Choice of Cost Object Example If the number of taxis owned by a taxi company is the cost object, annual taxi registration and license fees would be variable costs. If miles driven during a year on a particular taxi is the cost object, registration and license fees for that taxi are fixed costs.

Time Span Whether a cost is variable or fixed with respect to a particular activity depends on the time span. More costs are variable with longer time spans.

Relevant Range Variable and fixed cost behavior patterns are valid for linear cost functions only within the given relevant range. Costs may behave nonlinear outside the range.

Cost Estimation What is cost estimation? It is the attempt to measure a past cost relationship between costs and the level of an activity. Past cost-behavior functions can help managers make more accurate cost predictions.

The Cause-and-Effect Criterion In Choosing Cost Drivers Physical relationship Contractual agreements Implicitly established by logic

Learning Objective 3 Understand various approaches to cost estimation.

Cost Estimation Approaches 1. Industrial engineering method 2. Conference method 3. Account analysis method 4. Quantitative analysis methods

Industrial Engineering Method l A.k.a. work measurement method, estimated cost functions by analyzing the relationship between inputs and outputs in physical terms. (i.e. observing and measuring how it is done)……..may be very accurate but may be expensive and long!

Conference Method l Various departments share their experiences/views on how costs behave….not very accurate

Account Analysis Example The cost analyst uses experience and judgment to separate total costs (found in the ledgers) into fixed and variable. Eg Avisha & Co. sells software programs. Total sales = $390,000 The company sold 1,000 programs.

Account Analysis Example Cost of goods sold = $130,000 Manager’s salary = $60,000 Secretary’s salary = $29,000 Commissions = 12% of sales What is the total fixed cost? $60,000 + $29,000 = $89,000 What is the fixed cost per unit sold?

Account Analysis Example $89,000 ÷ 1,000 = $89.00 What is the variable cost per unit sold? Cost of goods sold: $130,000 Commissions: $390,000 ×.12 = $46,800 ($130,000 + $46,800) ÷ 1,000 = $176.80

Quantitative Analysis Methods l Uses a formal mathematical method to fit cost functions to past data observations E.g. 1 High-Low Methods E.g. 2 Regression Methods

Learning Objective 4 Outline six steps in estimating a cost function on the basis of past cost relationships.

Steps In Estimating A Cost Function Step 1: Choose the dependent variable. Step 2: Identify the independent variable cost driver(s). Step 3: Collect data on the dependent variable and the cost driver(s).

Steps In Estimating A Cost Function Step 5: Estimate the cost function. Step 6: Evaluate the estimated cost function. Step 4: Plot the data.

High-Low Method Example High capacity December: 55,000 machine-hours Cost of electricity: $80,450 Low capacity September: 30,000 machine-hours Cost of electricity: $64,200 What is the variable rate?

High-Low Method Example ($80,450 – $64,200) ÷ (55,000 – 30,000) $16,250 ÷ 25,000 = $0.65 What is the fixed cost?

High-Low Method Example $80,450 = Fixed cost + (55,000 × $0.65) Fixed cost = $80,450 – $35,750 = $44,700 $64,200 = Fixed cost + (30,000 × $0.65) Fixed cost = $64,200 – $19,500 = $44,700 y = a + bx y = $44,700 + ($0.65 × Machine-hours) Note - This method uses only two data Points to estimate the cost function.

Regression Analysis It is used to measure the average amount of change in a dependent variable, such as electricity, that is associated with unit increases in the amounts of one or more independent variables, such as machine-hours. Note - Regression analysis uses all available data to estimate the cost function.

Regression Analysis Simple regression analysis estimates the relationship between the dependent variable and one independent variable. Multiple regression analysis estimates the relationship between the dependent variable and multiple independent variables.

Regression Analysis The regression equation and regression line are derived using the least-squares technique. The objective of least-squares is to develop estimates of the parameters a and b.

Regression Analysis The vertical difference (residual term) measures the distance between the actual cost and the estimated cost for each observation. The regression method is more accurate than the high-low method.

Learning Objective 5 Describe three criteria used to evaluate and choose cost drivers.

Criteria to Evaluate and Choose Cost Drivers Economic plausibility Goodness of fit Slope of the regression line

Goodness of Fit The coefficient of determination (r 2 ) expresses the extent to which the changes in (x) explain the variation in (y). An (r 2 ) of 0.80 indicates that more than 80% of the change in the dependent variable can be explained by the change in the independent variable.

Slope of Regression Line A relatively steep slope indicates a strong relationship between the cost driver and costs. A relatively flat regression line indicates a weak relationship between the cost driver and costs.

Slope of Regression Line The closer the value of the correlation coefficient (r) to ±1, the stronger the statistical relation between the variables. As (r) approaches +1, a positive relationship is implied, meaning the dependent variable (y) increases as the independent variable (x) increases.

Slope of Regression Line As (r) approaches –1, a negative, or inverse, relationship is implied, meaning the dependent variable (y) decreases as the independent variable (x) increases. Example

Learning Objective 6 Explain and give examples of nonlinear cost functions.

Nonlinearity and Cost Functions A nonlinear cost function is a cost function in which the graph of total costs versus the level of a single activity is not a straight line within the relevant range. Reasons include: Economies of scale Quantity discounts Step cost functions

Nonlinearity and Cost Functions Economies of scale in advertising may enable an advertising agency to double the number of advertisements for less than double the cost. Quantity discounts on direct materials purchases produce a lower cost per unit purchased with larger orders.

Nonlinearity and Cost Functions A step function is a cost function in which the cost is constant over various ranges of the level of activity, but the cost increases by discrete amounts as the level of activity changes from one range to the next.

Learning Objective 7 Distinguish the cumulative average-time learning model from the incremental unit-time learning model.

Learning Curves A learning curve is a function that shows how labor-hours per unit decline as units of output increase.

Experience Curve This is a function that shows how the costs per unit in various value chain areas decline as units produced and sold increase.

Cumulative Average-Time Learning Model Cumulative average time per unit is reduced by a constant percentage each time the cumulative quantity of units produced is doubled.

Incremental Unit-Time Learning Model The time needed to produce the last unit is reduced by a constant percentage each time the cumulative quantity of units produced is doubled.

Learning Objective 8 Be aware of data problems encountered in estimating cost functions.

Data Collection and Adjustment Issues The ideal database for cost estimation has two characteristics: 1. It contains numerous reliably measured observations of the cost driver(s) and the cost that is the dependent variable. 2. It considers many values for the cost driver that span a wide range.

Data Collection and Adjustment Issues…problems Time periods do not match. Fixed costs are allocated as if they were variable. Data are either not available or not reliable. Inflation may play a role.

Data Collection and Adjustment Issues...problems Extreme values of observations occur from errors in recording costs. Analysts should adjust or eliminate unusual observations before estimating a cost relationship. There is no homogeneous relationship. The relationship between the cost driver and the cost is not stationary.

Data Collection and Adjustment Issues The most difficult task in cost estimation is collecting high-quality, reliably measured data on the dependent variable and the cost driver(s).